450.11 Four Sets of Axes of Spin: The omni-equi-edged and
radiused vector
equilibrium is omnisymmetrical, having 12 vertexes,
six square faces, eight triangular
faces, and 24 edges for a total of 50 symmetrically
positioned topological features. These
four sets of unique topological aspects of the vector
equilibrium provide four different sets
of symmetrically positioned polar axes of spin to generate
the 25 great circles of the
vector equilibrium. The 25 great circles of the vector
equilibrium are the equators of spin
of the 25 axes of the 50 unique symmetrically positioned
topological aspects of the vector
equilibrium.

450.12
Six of the faces of the vector equilibrium are square,
and they are only
cornerjoined and symmetrically arrayed around the vector
equilibrium in respect to one
another. We can pair the six opposite square faces so
that there are three pairs, and we can
interconnect their opposite centers of area to provide
three axes, corresponding to the
XYZ coordinates of Cartesian geometry. We can spin the
vector equilibrium on each of
these three intersymmetrically positioned axes of square
symmetry to produce three
equators of spin. These axes generate the set of three
intersymmetrical great-circle
equators of the vector equilibrium. Together the three
great circles subdivide the vector
equilibrium into eight octants.

450.13
There are also eight symmetrically arrayed triangular
faces of the vector
equilibrium. We can pair the symmetrically opposite
triangular faces so that there are four
pairs, and we can interconnect their opposite centers
of area to provide four
intersymmetrically positioned axes. We can spin the
vector equilibrium on each of these
four axes of symmetry to produce four intersymmetrical
equators of spin. These axes
generate the set four intersymmetrical great-circle
equators of the vector equilibrium.

450.14
When the 12 intersymmetrically positioned vertexes
of the vector equilibrium
are polarly interconnected, the lines of most economical
interconnection provide six
symmetrically interpositioned axes of spin. These six
axes generate the set of six
intersymmetrical great-circle equators of the vector
equilibrium.

450.15
We may also most economically interconnect the 24
polarly opposed
midpoints of the 24 intersymmetrically arrayed edges
of the vector equilibrium to provide
12 sets of intersymmetrically positioned axes of spin.
These axes generate the set of twelve
intersymmetrical great-circle equators of the vector
equilibrium.

450.16
As described, we now have sum-totally three square-face-centered
axes, plus
four triangular-face-centered axes, plus six vertex-centered
axes, plus 12 edge-centered
axes (3 + 4 + 6 + 12 = 25). There are a total of 25
complexedly intersymmetrical great
circles of the vector equilibrium.

451.01
It is a characteristic of all the 25 great circles
that each one of them goes
through two or more of the vector equilibrium's 12 vertexes.
Four of the great circles go
through six vertexes; three of them go through four
vertexes; and 18 of them go through
two vertexes.

451.02
We find that all the sets of the great circles that
can be generated by all the
axes of symmetry of the vector equilibrium go through
the 12 vertexes, which
coincidentally constitute the only points of tangency
of closestpacked, uniform-radius
spheres. In omnidirectional closest packing, we always
have 12 balls around one. The
volumetric centers of the 12 uniformradius balls closest
packed around one nuclear ball
are congruent with the 12 vertexes of the vector equilibrium
of twice the radius of the
closest-packed spheres.

451.03
The network of vectorial lines most economically interconnecting
the
volumetric centers of 12 spheres closest packed around
one nuclear sphere of the same
radius describes not only the 24 external chords and
12 radii of the vector equilibrium but
further outward extensions of the system by closest
packing of additional uniform-radius
spheres omnisurrounding the 12 spheres already closest
packed around one sphere and
most economically interconnecting each sphere with its
12 closest-packed tangential
neighbors, altogether providing an isotropic vector
matrix, i.e., an omnidirectional
complex of vec torial lines all of the same length and
all interconnected at identically
angled convergences. Such an isotropic vector matrix
is comprised internally entirely of
triangular-faced, congruent, equiedged, equiangled octahedra
and tetrahedra. This
isotropic matrix constitues the omnidirectional grid.

451.04
The basic gridding employed by nature is the most
economical
agglomeration of the atoms of any one element. We find
nature time and again using this
closest packing for most economical energy coordinations.

452.00 Vector Equilibrium: Great-Circle Railroad Tracks of
Energy

452.01
The 12 points of tangency of unit-radius spheres in
closest packing, such as
is employed by any given chemical element, are important
because energies traveling over
the surface of spheres must follow the most economical
spherical surface routes, which are
inherently great circle routes, and in order to travel
over a series of spheres, they could
pass from one sphere to another only at the 12 points
of tangency of any one sphere with
its closestpacked neighboring uniform-radius sphere.

452.02
The vector equilibrium's 25 great circles, all of
which pass through the 12
vertexes, represent the only "most economical lines"
of energy travel from one sphere to
another. The 25 great circles constitute all the possible
"most economical railroad tracks"
of energy travel from one atom to another of the same
chemical elements. Energy can and
does travel from sphere to sphere of closest-packed
sphere agglomerations only by
following the 25 surface great circles of the vector
equilibrium, always accomplishing the
most economical travel distances through the only 12
points of closestpacked tangency.

452.03
If we stretch an initially flat rubber sheet around
a sphere, the outer spherical
surface is stretched further than the inside spherical
surface of the same rubber sheet
simply because circumference increases with radial increase,
and the more tensed side of
the sheet has its atoms pulled into closerradial proximity
to one another. Electromagnetic
energy follows the most highly tensioned, ergo the most
atomically dense, metallic element
regions, wherefore it always follows great-circle patterns
on the convex surface of metallic
spheres. Large copper-shelled spheres called Van De
Graaff electrostatic generators are
employed as electrical charge accumulators. As much
as two million volts may be
accumulated on one sphere's surface, ultimately to be
discharged in a lightninglike leap-
across to a near neighbor copper sphere. While a small
fraction of this voltage might
electrocute humans, people may walk around inside such
high-voltage-charged spheres
with impunity because the electric energy will never
follow the concave surface paths but
only the outer convex great-circle paths for, by kinetic
inherency, they will always follow
the great-circle paths of greatest radius.

452.04
You could be the little man in Universe who always
goes from sphere to
sphere through the points of intersphere tangencies.
If you lived inside the concave surface
of one sphere, you could go through the point of tangency
into the next sphere, and you
could go right through Universe that way always inside
spheres. Or you could be the little
man who lives on the outside of the spheres, always
living convexly, and when you came
to the point of tangency with the next sphere, you could
go on to that next sphere
convexly, and you could go right through Universe that
way. Concave is one way of
looking at Universe, and convex is another. Both are
equally valid and cosmically
extensive. This is typical of how we should not be fooled
when we look at spheres __or by
just looking at the little local triangle on the surface
of our big sphere and missing the big
triangle6 always polarly complementing it and defined
by the same three edges but
consisting of all the unit spherical surface area on
the outer side of the small triangle's
three edges. These concave-convex, inside-out, and surface-area
complementations are
beginning to give us new clues to conceptual comprehending.

452.05
As was theoretically indicated in the foregoing energy-path
discoveries, we
confirm experimentally that electric charges never travel
on the concave side of a sphere:
they always stay on the convex surface. In the phenomenon
of electroplating, the convex
surfaces are readily treated while it is almost impossible
to plate the concave side except
by use of a close matrix of local spots. The convex
side goes into higher tension, which
means that it is stretched thinner and tauter and is
not only less travel-resistant, but is more
readily conductive because its atoms are closer to one
another. This means that
electromagnetic energy automatically follows around
the outside of convex surfaces. It is
experimentally disclosed and confirmed that energy always
seeks the most economical,
ergo shortest, routes of travel. And we have seen See
Sec. 810,
"One Spherical Triangle
Considered as Four." that the shortest intersphere or
interatom routes consist exclusively
of the 25 great-circle geodesic-surface routes, which
transit the 12 vertexes of the vector
equilibrium, and which thus transit all the possible
points of tangency of closest-packed
spheres.

452.06
There always exists some gap between the closest-packed
spheres due to the
nuclear kinetics and absolute discontinuity of all particulate
matter. When the 12 tangency
gaps are widened beyond voltage jumpability, the eternally
regenerative conservation of
cosmic energy by pure generalized principles will reroute
the energies on spherically
closed great-circle "holding patterns" of the 25 great
circles, which are those produced by
the central-angle foldings of the four unique great-circle
sets altogether comprising the
vector equilibrium's 25 great circles.

452.07
High energy charges in energy networks refuse to take
the longest of the
two great-circle arc routes existing between any two
spherical points. Energy always tends
to "short-circuit," that is, to complete the circuit
between any two spherical surface points
by the shortest great-circle arc route. This means that
energy automatically triangulates via
the diagonal of a square or via the triangulating diagonals
of any other polygons to which
force is applied. Triangular systems represent the shortest,
most economical energy
networks. The triangle constitutes the self-stabilizing
pattern of complex kinetic energy
interference occasioned angular shuntings and three-fold
or more circle interaction
averaging of least-resistant directional resultants,
which always trend toward equiangular
configurations, whether occurring as free radiant energy
events or as local self-
structurings.